Problem: If $a + b + c = 7$ and $x + y + z = 3$, what is $-2a - 2b - 3z - 3y - 2c - 3x$ ?
Solution: $= -2a - 2b - 2c - 3x - 3y - 3z$ $= (-2) \cdot (a + b + c) + (-3) \cdot (x + y + z)$ $= (-2) \cdot (7) + (-3) \cdot (3)$ $= -14 - 9$ $= -23$